On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel

Razaviyayn, Meisam; Lyubeznik, Gennady; Luo, Zhi-Quan

doi:10.1109/tsp.2011.2173683

Cited by 240 publications

(126 citation statements)

References 14 publications

(55 reference statements)

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“…The conjectured correspondence between proper/improper systems and feasible/infeasible systems is settled completely in one direction, and partially in the other direction, in recent works by Bresler et al in [13] and Razaviyayn et al in [14], who show that: 1. Improper systems are infeasible [13,14]. 2.…”

Section: Feasibility Of Linear Interference Alignment Without Time/frmentioning

confidence: 99%

Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

Wang

Gou

Jafar

2012

2012 IEEE International Symposium on Information Theory Proceedings

260

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We show that the 3-user M T × M R MIMO interference channel where each transmitter is equipped with M T antennas and each receiver is equipped with M R antennas has d(M, N ) = min M 2−1/κ , N 2+1/κ degrees of freedom (DoF) normalized by time, frequency, and space dimensions, whereWhile the DoF outer bound of d(M, N ) is established for every M T , M R value, the achievability of d(M, N ) DoF is established in general subject to a normalization with respect to spatial-extensions, i.e., the scaling of the number of antennas at all nodes. Specifically, we show that qd(M, N ) DoF are achievable for the 3-user qM T × qM R MIMO interference channel, for some positive integer q which may be seen as a spatial-extension factor. q is the scaling factor needed to make the value qd(M, N ) an integer. Given spatial-extensions, the achievability relies only on linear beamforming based interference alignment schemes and requires neither channel extensions nor channel variations in time or frequency. In the absence of spatial extensions, it is shown through examples how essentially the same interference alignment scheme may be applied over time-extensions over either constant or time-varying channels. The central new insight to emerge from this work is the notion of subspace alignment chains as DoF bottlenecks. The subspace alignment chains are instrumental both in identifying the extra dimensions to be provided by a genie to a receiver for the DoF outer bound, as well as in the construction of the optimal interference alignment schemes.The DoF value d(M, N ) is a piecewise linear function of M, N , with either M or N being the bottleneck within each linear segment while the other value contains some redundancy, i.e., it can be reduced without reducing the DoF. The corner points of these piecewise linear segments correspond to two sets, A = {1/2, 2/3, 3/4, · · · } and B = {1/3, 3/5, 5/7, · · · }. The set A contains all those values of M/N and only those values of M/N for which there is redundancy in both M and N , i.e., either can be reduced without reducing DoF. The set B contains all those values of M/N and only those values of M/N for which there is no redundancy in either M or N , i.e., neither can be reduced without reducing DoF. Because A and B represent settings with maximum and minimum redundancy, essentially they are the basis for the DoF outer bounds and inner bounds, respectively.Our Our results show that M/N ∈ A are the only values for which there is no DoF benefit of joint processing among co-located antennas at the transmitters or receivers. This may also be seen as a consequence of the maximum redundancy in the M/N ∈ A settings.

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Section: Feasibility Of Linear Interference Alignment Without Time/frmentioning

confidence: 99%

Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

Wang

Gou

Jafar

2012

2012 IEEE International Symposium on Information Theory Proceedings

260

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“…Remark 3.6 (Backward Compatible to [12], [14], and [15]): If we further assume that d = 1, then d|M k , d|N k for all k ∈ {1, ..., K}. In this case, Cor.…”

Section: Linearly Independent Algebraically Independentmentioning

confidence: 99%

“…Similarly, if we require both N k and M k are divisible by d, Cor. 3.4 is reduced to the feasibility conditions given by [14], [15].…”

Section: Linearly Independent Algebraically Independentmentioning

confidence: 99%

“…7]. This work has been extended to the multiple stream case by two parallel works [13], and [14,15], respectively. The first approach in [13] established some necessary conditions for the IA feasibility condition for general network topology by analyzing the dimension of the algebraic varieties [10].…”

Section: Introductionmentioning

confidence: 99%

“…The authors further showed that these conditions are also sufficient when the number of antennas and data streams at every node are identical. The second approach in [14], [15] established a similar necessary conditions for the IA feasibility problem based on algebraic independence between the IA constraints. The authors further proved that these conditions are also sufficient when the number of data stream at every node is the same and the number of antennas at every node is divisible by the number of data streams.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The feasibility conditions of interference alignment for MIMO interference networks

Ruan

Lau

Win

2012

2012 IEEE International Symposium on Information Theory Proceedings

108

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Abstract-Interference alignment (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition matches with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.

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Interference‐resilient spectrum sharing with collision detection and data recovery for cognitive radio networks

Imran

Loan

Mahmood

2020

Int J Communication

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Summary Data recovery under collision of primary/secondary users in cognitive radio networks is largely an unaddressed problem. Existing approaches require either (a) retransmissions, (b) interference‐free alignment of transmission parameters, or (c) prior knowledge for data recovery. In contrast to the existing approaches, the paper proposes estimation of channel state information based on received collided frames and recommends techniques for spectrum sharing, collision detection, and data recovery. Specifically, based on estimated channel vector, interference‐resilient spectrum‐sharing protocol and techniques are proposed for (a) identification of primary user (PU) activity before (or during) secondary user's (SU's) transmission, (b) MIMO channel estimation under collision, (c) optimal pilot permutation, and (d) interference cancellation (with/without receiver diversity). Results are reported for different baseband modulation techniques under frequency selective/flat fading channel scenarios that demonstrate the efficacy of a proposed work.

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On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel

Cited by 240 publications

References 14 publications

Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

The feasibility conditions of interference alignment for MIMO interference networks

Interference‐resilient spectrum sharing with collision detection and data recovery for cognitive radio networks

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